A brother-sister blues-punk duo, Joe Gideon & the Shark differ from The White Stripes in at least three crucial ways. One is that singer-guitarist Joe – a veteran of Bikini Atoll – is often outshone by his sister Viva (aka The Shark), particularly in a live setting. A second is that nobody's yet produced a marriage certificate. A third is that these two are no Luddites.

Viva not only drums and plays keyboards, but sings backing vocals through a delay pedal and fills out the sound with programmed beats and sequences. Without his sister, Joe would be a bit of a busker, albeit one with a gift for an arresting one-liner. Without Joe, Viva would be a prim English Peaches who once competed at the Olympics as a rhythmic gymnast. Truly, the mind boggles.

Though a Londoner, Gideon is steeped in Americana. He sings in a southern US drawl and in an argot drawn from Beatnik novels, while his riffs channel 30s blues, 50s rock 'n' roll and the trashy punk primitivism of The Cramps. Originality might not be his strong suit, but he's redeemed by the conspiratorial urgency with which he delivers his lyrics and the poeticism that runs through them.

On 'Civilisation' he unfurls an improbable life story that's an amusing mix of self-aggrandisement and self-abasement. “Wrote a book which was a spectacular success, spent all my earnings on weed and crystal meth,” he declares at one point. Later, he opens 'True Nature' with this gem: “She was a real bad judge of character – as in she saw the good in everyone.” Bar-room tales of wine, women and wickedness are naturally abundant, but there's an innocence to Gideon that endears him to you. The album's best song, 'Hide and Seek', tells the tale of a childhood game gone horribly wrong.

'Hide and Seek' damn near set East London alight when Joe Gideon & the Shark supported Wire at Cargo in February, and on record it's no less potent. Built on a Hammer Horror piano motif, it impresses in every way. The lyrics are wry and witty (“What I didn't like about him was the way he smelled,” runs the opening line), while Viva's looped backing vocals are hypnotic, and there's a heart-stopping moment when Joe delivers a terrified shout of “I realised I was lost in a game!” over a sudden burst of grinding guitars and crashing drums.

'Hide and Seek', the seventh of the album's nine songs, is the climax of an album focused largely on irreverent, comical character studies, with song titles including 'Daughter of a Loony' and 'Johan Was a Painter and Arsonist'. As the album draws to a close, Gideon switches to home-spun philosophy, and the title of the penultimate track brings a cryptic but comforting declaration: 'Anything You Love That Much, You Will See Again'. Musically gentle, this track eases us down from the peak of 'Hide and Seek' and seems to bring proceedings to a logical conclusion.

Irritatingly, however, the album ends not there but with the pointlessly tacked-on 'Pale Blue Dot', in which nothing at all happens. But this is the only serious misstep in an album that's witty, intense, dynamic and – in its mix of blues and beats – musically inventive at times. Joe Gideon & the Shark are breathing new life into the increasingly familiar boy-girl rock duo format, recently drawn into disrepute by The Ting Tings. Let's hope the mainstream takes the bait.